Summary Structures for Frequency Queries on Large Transaction Sets

As large-scale databases become commonplace, there has been signi cant interest in mining them for commercial purposes. One of the basic tasks that underlies many of these mining operations is querying of transaction sets for frequencies of speci ed attribute values. The size of these databases makes it important to develop summary structures capable of high compression ratios as well as supporting fast frequency queries. The nature of the problem and its di erences with respect to traditional text compression allows very high compression ratios. In this paper, we propose a binary trie-based summary structure for representing transaction sets. We demonstrate that this trie structure, when augmented with an appropriate set of horizontal pointers, can support frequency queries several orders of magnitude faster than raw transaction data. We improve the memory characteristics of our scheme by compressing the trie into a Patricia trie and demonstrate that this does not have a signi cant adverse e ect on frequency query time. We further reduce the size of this trie by selectively pruning branches to compute a \dominant" trie that is capable of approximate frequency querying. The complement trie called the \deviant" trie is also useful in many data mining applications. Recompressing the \dominant" trie into a Patricia trie results in further compression of the trie. Finally, we demonstrate that our binary compressed trie structure has better memory (compression) characteristics compared to related schemes. We support our claims with experimental results on datasets from the IBM synthetic association data generator. This work is supported in part by the National Science Foundation grants EIA-9806741, ACI9875899, and ACI-9872101. Computing equipment used for this work was supported by National Science Foundation MRI grant EIA-9871053 and by the Intel Corp.